pricesforindividualassets,thesecondistoestimatethebetas
fromfundamentals,andthethirdistouseaccountingdata.
We describe all three approaches in this subsection.
Historical Market Betas
Thisistheconventionalapproachforestimatingbetasused
by most services and analysts. For firms that have been
publicly traded for a length of time, it is relatively
straightforward to compute returns that an investor would
havemadeonitsequityinweeklyormonthlyintervalsover
thatperiod.Thesereturnscanthenberelatedtoreturnsona
proxyforthemarketportfoliotogetabetainthecapitalasset
pricingmodel,ortomultiplemacroeconomicfactorstoget
betas in the multifactor models, or put through a factor
analysistoyieldbetasforthearbitragepricingmodel.The
standard procedure for estimating the CAPM beta is to
regress
25 stock returns (Rj) against market returns (Rm):
where
a= Intercept from the regression
b= Slope of the regression = Covariance(Rj,Rm)/σm 2
Theslope ofthe regressioncorresponds to thebetaof the
stockandmeasurestheriskinessofthestock.Thisslope,like
anystatistical estimate,comeswith astandarderror,which
revealsjust hownoisy theestimateis,and canbe usedto
arrive at confidence intervals for the “true” beta value.